Learning Objectives 1.DEFINE A CALL OPTION AND A PUT OPTION, AND DESCRIBE THE PAYOFF FUNCTION FOR EACH OF THESE OPTIONS. 2.LIST AND DESCRIBE THE VARIABLES THAT AFFECT THE VALUE OF AN OPTION. CALCULATE THE VALUE OF A CALL OPTION AND OF A PUT OPTION.
Learning Objectives 4.NAME SOME OF THE REAL OPTIONS THAT OCCUR IN BUSINESS AND EXPLAIN WHY TRADITIONAL NPV ANALYSIS DOES NOT ACCURATELY INCORPORATE THEIR VALUES. 5.DESCRIBE HOW THE AGENCY COSTS OF DEBT AND EQUITY ARE RELATED TO OPTIONS. 6.EXPLAIN HOW OPTIONS CAN BE USED TO MANAGE A FIRM’S EXPOSURE TO RISK.
Financial Options o A financial option is a derivative security in that its value is derived from the value of another asset. o The owner of a financial option has the right, but not the obligation, to buy or sell an asset on or before a specified date for a specified price. o The asset that the owner has a right to buy or sell is known as the underlying asset.
Financial Options o The last date on which an option can be exercised is called the exercise date or expiration date, and the price at which the option holder can buy or sell the asset is called the exercise price or strike price.
Financial Options o CALL OPTIONS A call option gives the owner the right to buy, or “call,” the underlying asset. Once the asset price goes above the exercise price, the value of the call option at exercise increases dollar for dollar with the price of the underlying asset. The buyer pays the seller a fee to purchase the option. This fee, which is known as the call premium, makes the total return to the seller positive when the price of the underlying asset is near or below the exercise price.
Financial Options o PUT OPTIONS The owner of a put option has the right to sell the underlying asset at a pre-specified price. The payoff function for the owner of a put option is similar to that of a call option, but it is the reverse in the sense that the owner of a put option profits if the price of the underlying asset is below the exercise price. The owner of a put option will not want to exercise the option if the price of the underlying asset is above the exercise price.
Financial Options o PUT OPTIONS When the value of the underlying asset is below the exercise price, however, the owner of the put option will find it profitable to exercise the option. The payoff for the seller of the put option is negative when the price of the underlying asset is below the exercise price. The seller of a put option hopes to profit from the fee, or put premium, that he or she receives from the buyer of the put option.
Financial Options o AMERICAN, EUROPEAN, AND BERMUDAN OPTIONS Options that can only be exercised on the expiration date are known as European options. American options can be exercised at any point in time on or before the expiration date. Bermudan options can be exercised only on specific dates during the life of the option.
Financial Options o MORE ON THE SHAPES OF OPTION PAYOFF FUNCTIONS The payoff functions for options are not straight lines for all possible values of the underlying asset. Each payoff function has a “kink” at the exercise price which exists because the owner of the option has a right, but not the obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it expire.
Option Valuation o It is more complicated to determine the value of an option at a point in time before the expiration date because we don’t know exactly how the value of the underlying asset will change over time, and therefore we don’t know if it will make sense to exercise the option.
Option Valuation o LIMITS ON OPTION VALUATION We know that the value of a call option can never be less than zero, since the owner of the option can always decide not to exercise it if doing so is not beneficial. The value of a call option can never be greater than the value of the underlying asset since it would not make sense to pay more for the right to buy an asset than you would pay for the asset itself.
Option Valuation o LIMITS ON OPTION VALUATION The value of a call option prior to expiration will never be less than the value of that option at expiration because there is always a possibility that the value of the underlying asset will be greater than it is today at some time before the option expires.
Option Valuation o LIMITS ON OPTION VALUATION When we consider the value of a call option at some point prior to expiration, we must compare the current value of the underlying asset with the present value of the exercise price, discounted at the risk-free rate. The present value of the exercise price is the amount an investor would have to invest in risk- free securities at any point prior to the expiration date to ensure that he or she would have enough money to exercise the option when it expires.
Option Valuation o VARIABLES THAT AFFECT OPTION VALUES The higher the current value of the underlying asset, the more likely it is that the value of the asset will be above the exercise price when the call option expires. The opposite relation applies to the exercise price. The lower the exercise price, the more likely that the value of the underlying asset will be higher than the exercise price when the option nears expiration.
Option Valuation o VARIABLES THAT AFFECT OPTION VALUES The higher the current value of the asset, the greater the likely difference between the value of the asset and the exercise price when the option expires. In addition, the lower the exercise price, the more valuable the option is likely to be at expiration.
Option Valuation o VARIABLES THAT AFFECT OPTION VALUES The greater the volatility of the underlying asset value, the higher the value of a call option on the asset prior to valuation. The intuition here is that the value of an option will increase more when the value of the underlying asset goes up than it will decrease when the value of the underlying asset goes down; this means that a greater potential change in the underlying price will be more beneficial to the value of the option.
Option Valuation o VARIABLES THAT AFFECT OPTION VALUES The greater the time to maturity, the more the value of the underlying asset is likely to change by the time the option expires; this increases the value of an option. The time until the expiration affects the value of a call option through its effect on the volatility of the value of the underlying asset. The value of a call option increases with the risk-free rate.
Option Valuation o VARIABLES THAT AFFECT OPTION VALUES Exercising a call option involves paying cash in the future for the underlying asset. The higher the interest rate, the lower the present value of the amount that the owner of a call option will have to pay to exercise it, which translates into value for the owner of the option.
Option Valuation o THE BINOMIAL OPTION PRICING MODEL This simple model assumes that the underlying asset will have one of only two possible values when the option expires. The value of the underlying asset will either increase to some value above the exercise price or decrease to some value below the exercise price.
Option Valuation o THE BINOMIAL OPTION PRICING MODEL To solve for the value of the call option using this model, we must assume that investors have no arbitrage opportunities with regard to this option. Arbitrage is the act of buying and selling assets in a way that yields a return above that suggested by the Security Market Line (SML). To value the call option in our simple model, we will first create a portfolio that consists of the asset underlying the call option and a risk-free loan.
Option Valuation o THE BINOMIAL OPTION PRICING MODEL The relative investments in these two assets will be selected so that the combination of the asset and the loan have the same cash flows as the call option when it expires, regardless of whether the value of the underlying asset goes up or down. This is called a replicating portfolio, since it replicates the cash flows of the option.
Option Valuation o THE BINOMIAL OPTION PRICING MODEL The replicating portfolio will consist of: “x” shares of the underlying stock; a risk-free loan with a face value of “y”. The value of the call option can be calculated as follows: Solve for the values of “x” and “y”. Multiply the current cost of the underlying stock by “x”. Subtracting “y” from the above amount will yield the value of the call option.
Option Valuation o PUT-CALL PARITY Although there are other methods, the value of a put option can be calculated by the relationship of a put to a call option with the same maturity and exercise price. This relation is called the put-call parity.
Option Valuation o PUT-CALL PARITY where: P is the value of the put option C is the value of the call option X is the exercise price V is the current value of the underlying asset e is the exponential function
Option Valuation o Put-call parity example: What is the value of ABC corporation put option if C=$5.95, X=$55, r=0.05, t=1, and V=$50? P = $5.95 + $55e-(0.05)(1) - $50 = $5.95 + $52.32 - $50 = $8.27
Option Valuation o VALUING OPTIONS ASSOCIATED WITH THE FINANCIAL SECURITIES THAT FIRMS ISSUE Financial options are often included in the financial securities that firms issue and they make the valuation of those securities more complicated. The key principle that is used in valuing securities with options is known as the principle of value additivity. It states that if two independent assets are bundled together, the total value of both assets equals the sum of their individual values.
Real Options o Real options are options on real assets. o NPV analysis does not adequately reflect the value of real options. o It might not always be possible to directly estimate the value of the real options associated with a project, it is important to recognize that they exist when we perform a project analysis.
Real Options o OPTIONS TO DEFER INVESTMENT An example from the text is that of the Russian government and an oil field development project. The Russian government waited to see what happened to the price of oil before deciding to exercise its option to acquire an ownership interest in the Sakhalin II project.
Real Options o OPTIONS TO DEFER INVESTMENT The underlying asset in this option is the stream of cash flows that the developed oil field would produce, while the exercise price is the amount of money that the company would have to spend to develop it (drill the well and build any necessary infrastructure). The value of an option to defer investment is not reflected in a NPV analysis as it does not allow for the possibility of deferring an investment decision.
Real Options o OPTIONS TO MAKE FOLLOW-ON INVESTMENTS Some projects open the door to future business opportunities that would not otherwise be available. This type of real option is an option to make follow-on investments. Options to make follow-on investments are inherently difficult to value because, at the time we are evaluating the original project, it may not be obvious what the follow-on projects will be.
Real Options o OPTIONS TO MAKE FOLLOW-ON INVESTMENTS Even if we know what the projects will be, we are unlikely to have enough information to estimate what they are worth. Projects that lead to investment opportunities that are consistent with a company’s overall strategy are more valuable than otherwise similar projects that do not.
Real Options o OPTIONS TO CHANGE OPERATIONS Are related to the flexibility that managers have once an investment decision has been made. These include the option to change operations and to abandon a project; they affect the NPV of a project and must be taken into account at the time the investment decision is made. The changes that managers might make can involve something as simple as reducing output if prices decline or increasing output if prices increase.
Real Options o OPTIONS TO ABANDON PROJECTS An option to abandon a project is the ability to choose to terminate a project by shutting it down. Management will save money that would otherwise be lost if the project kept going. The amount saved represents the gain from exercising this option.
Real Options o CONCLUDING COMMENTS ON NPV ANALYSIS AND REAL OPTIONS In order to use NPV analysis to value the option to expand operations, we would not only have to estimate all the cash flows associated with the expansion but would also have to estimate the probability that we would actually undertake the expansion and determine the appropriate rate at which to discount the value of the expansion back to the present.
Agency Costs o Agency conflicts between stockholders and debt holders and between stockholders and managers arise because the interests of stockholders, lenders (creditors), and managers are not perfectly aligned. o One reason is that the claims that they have against the cash flows produced by the firm have payoff functions that look like different types of options.
Agency Costs o AGENCY COSTS OF DEBT The payoff functions for stockholders and lenders (creditors) differ as do the payoff functions for different options. The payoff function for the stockholders looks exactly like that of the owner of a call option, where the exercise price is the amount owed on the loan and the underlying asset is the firm itself.
Agency Costs o AGENCY COSTS OF DEBT If the value of the firm exceeds the exercise price, the stockholders will choose to exercise their option; and if it does not exceed the exercise price, they will let their option expire unexercised. One way to think about the payoff function for the lenders is that when they lend money to the firm, they are essentially selling a put option to the stockholders.
Agency Costs o AGENCY COSTS OF DEBT This option gives the stockholders the right to “put” the assets to the lenders for an exercise price that equals the amount they owe. When the value of the firm is less than the exercise price, the stockholders will exercise their option by defaulting.
Agency Costs o AGENCY COSTS OF DEBT The Dividend Payout Problem The incentives that stockholders of a leveraged firm have to pay themselves dividends arise because of their option to default. If a company faces some realistic risk of going bankrupt, the stockholders might decide that they are better off taking money out of the firm by paying themselves dividends. This situation can arise because the stockholders know that the bankruptcy laws limit their possible losses.
Agency Costs o AGENCY COSTS OF DEBT The Asset-Substitution Problem When bankruptcy is possible, stockholders have an incentive to invest in very risky projects, some of which might even have negative NPVs. Stockholders have this incentive because they receive all of the benefits if things turn out well but do not bear all of the costs if things turn out poorly.
Agency Costs o AGENCY COSTS OF DEBT The Underinvestment Problem Stockholders have incentives to turn down positive- NPV projects when all of the benefits are likely to go to the lenders. The problem arises from the differences in the payoff functions.
Agency Costs o AGENCY COSTS OF EQUITY Managers are hired to manage the firm on behalf of the stockholders but managers do not always act in the stockholders’ best interest. The payoff function for a manager can be quite different from that for stockholders. In fact, it can look a lot like that of a lender. If a company gets into financial difficulty and a manager is viewed as responsible, that manager could lose his or her job and find it difficult to obtain a similar job at another company.
Agency Costs o AGENCY COSTS OF EQUITY The most obvious way for a company to get into financial difficulty is to default on its debt. So, as long as a company is able to avoid defaulting on its debt, a manager has a reasonable chance of retaining his or her job.
Agency Costs o AGENCY COSTS OF EQUITY The fact that the payoff function for a manager resembles that of a lender means that managers, like lenders, have incentives to invest in less risky assets and to distribute less value through dividends and stock repurchases than the stockholders would like them to.
Options and Risk Management o Risk management typically involves hedging, or reducing the financial risks faced by a firm. o Options, along with other derivative instruments, such as forwards, futures, and swaps, are commonly used to reduce risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices.
Options and Risk Management o One interesting benefit of using options in this way is that they provide downside protection but do not limit the upside. This is just like buying insurance. Many insurance contracts are really little more than specialized put options. o Options and other derivative instruments can be used to manage commodity price risks, large swings in interest rates, risks associated with foreign exchange rates, as well as to manage risks associated with equity prices as occurs within defined benefit pension plans.